Defining parameters
| Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1296.p (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(864\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1296, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1344 | 0 | 1344 |
| Cusp forms | 1248 | 0 | 1248 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{4}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)